“This apparent departure from the familiar laws of thermodynamics is akin to our warm apple pie either cooling as expected or spontaneously bursting into flames, depending on the pie’s exact temperature when it is placed in the window,” said Hudson, the senior author of the study.

For chemists and physicists, cooling samples of charged particles, also called ions, makes them easier to control and study. So they use a similar approach — called buffer gas cooling — to lower the temperature of ions by trapping them and then immersing them in clouds of cold atoms. Collisions with the atoms cool the originally hot ions by transferring energy from the ions to the atoms — much the same way a warm pie is cooled next to the cold window, said Eric Hudson, associate professor of physics at UCLA.

The UCLA researchers have, for the first time, placed fundamental limits on the use of buffer gas cooling in “ion traps.” To perform their experiment, the researchers prepared a microscopic sample of laser cooled ions of the chemical element barium and immersed them in clouds of roughly 3 million laser-cooled calcium atoms. The researchers make molecules extremely cold under highly controlled conditions to reveal the quantum mechanical properties that are normally hidden.

The ions were trapped in an apparatus that levitates charged particles by using electric fields that oscillate millions of times per second, confining the ions to a region smaller than the width of a human hair. Both the atomic and ionic samples were brought to ultra-cold temperatures —just one-thousandth of a degree above absolute zero — via a technique in which the momentum of light in a laser is used to slow particle motion.

After allowing collisions between the atoms and ions to occur and the system to reach its final temperature, the physicists removed the calcium atoms and measured the temperature of the barium ions. The results, which show the existence of multiple final temperatures based on ion number and initial temperature, suggest that subtle non-equilibrium physics is at play.

The researchers trace these strange features to the heating and cooling rates which exist in the system — the peculiar temperature dependence of the interaction among multiple ions in an ion trap. Both simulation and theory support their experimental findings, and paint the buffer-gas cooling process as a fundamentally nuanced, non-equilibrium process rather than the straightforward equilibrium process it was originally understood to be.

Lead author Steven Schowalter, a graduate student researcher in Hudson’s laboratory and now a staff scientist at NASA’s Jet Propulsion Laboratory, said, “Our results demonstrate that you can’t just throw any buffer gas into your device — no matter how cold it is — and expect it to work as an effective coolant.”

Buffer gas cooling is crucial in fields ranging from forensics to the production of antimatter. Hudson’s research group has discovered important nuances that revise the current understanding of the cooling process, explain the difficulties encountered in previous cooling experiments and show a new path forward for creating ultra-cold ion samples. With this framework the researchers showed how troublesome effects can be overcome and even exploited to study the mechanisms at play in molecular motors and single-atom heat engines in a precisely controlled manner.

“Of course, this work does not violate the laws of thermodynamics, but it does demonstrate there are still some interesting, potentially useful things to learn about buffer gas cooling,” said John Gillaspy, a physics division program director at the National Science Foundation, which funds the research. “This is the sort of fundamental research that can really guide a wide range of more applied research efforts, helping other scientists and engineers to avoid going down dead-end paths and illuminating more fruitful directions they might take instead.”

In summary, they have presented a theoretical and experimental description of trapped ions immersed in a cold atomic gas, demonstrating the emergence of nonequilibrium behaviour, culminating in the observation of a blue-sky bifurcation in the ion steady-state temperature. The impact of this work is primarily twofold: first, the cooling power of a laser-cooled buffer gas is only sufficient to cool the translational motion of small numbers of trapped ions. This has serious implications for hybrid atom–ion traps, which are typically employed to study physics and chemistry at ultracold temperatures, and places limits on the ability to create and maintain cold samples of trapped ions using sympathetic cooling. If systems with larger numbers of ions are desired, the restricted cooling power necessitates the need for additional cooling, such as sympathetic cooling with co-trapped laser-cooled ions. Outside of hybrid trapping, these limitations may impact low-temperature chemical studies that use neutral gases to set reaction energies and the development of mass spectrometers, which use cold neutral gases to collisionally cool analyte ions for increased mass resolution. This work may also revise the viability of using cold neutral gases alone as an initialization step for molecular ion qubits in future quantum computation architecture. Additionally, the ion–ion heating rate applied in the present work should also be applicable to studies of bistability in laser-cooled trapped ions. Second, this work represents the first experimental realization of the rich non-equilibrium physics that can exist in hybrid traps. Given the precise control afforded by these systems and the ease of implementation of work protocols and dissipative mechanisms, hybrid systems may become precise tools with which to study the complex phenomena of systems existing far from equilibrium.

Abstract

Sympathetic cooling of trapped ions through collisions with neutral buffer gases is critical to a variety of modern scientific fields, including fundamental chemistry, mass spectrometry, nuclear and particle physics, and atomic and molecular physics. Despite its widespread use over four decades, there remain open questions regarding its fundamental limitations. To probe these limits, here we examine the steady-state evolution of up to 10 barium ions immersed in a gas of three-million laser-cooled calcium atoms. We observe and explain the emergence of nonequilibrium behaviour as evidenced by bifurcations in the ion steady-state temperature, parameterized by ion number. We show that this behaviour leads to the limitations in creating and maintaining translationally cold samples of trapped ions using neutral-gas sympathetic cooling. These results may provide a route to studying non-equilibrium thermodynamics at the atomic level.